Stereo Slant Discrimination of Planar 3D Surfaces: Standard vs. Planar Cross-Correlation

Abstract

Binocular stereo cues are important for discriminating 3D surface orientation, especially at near distances. We devised a single-interval task where observers discriminated the slant of a densely textured planar test surface relative to a textured planar surround reference surface. Although surfaces were rendered with correct perspective, the stimuli were designed so that the binocular cues dominated performance. Slant discrimination performance was measured as a function of the reference slant and the level of uncorrelated white noise added to the test-plane images in the left and right eye. We compared human performance with an approximate ideal observer (planar cross correlation, PCC) and two sub-ideal observers. The PCC observer uses the image in one eye and back projection to predict the test image in the other eye for all possible slants, tilts, and distances. The estimated slant, tilt, and distance are determined by the prediction that most closely matches the measured image in the other eye. The first sub-ideal observer (local PCC, LPCC) applies planar cross correlation over local neighborhoods and then pools estimates across the test plane. The second sub-optimal observer (standard cross correlation, SCC), uses only positional disparity information. We find that the ideal observer (PCC) and the first sub-ideal observer (LPCC) outperform the second sub-ideal observer (SCC), demonstrating the benefits of structural disparities. We also find that all three model observers can account for human performance, if two free parameters are included: a fixed small level of internal estimation noise, and a fixed overall efficiency scalar on slant discriminability. PrecisWe measured human stereo slant discrimination thresholds for accurately-rendered textured surfaces designed so that performance is dominated by binocular-disparity cues. We compared human performance with an approximate ideal observer and two sub-ideal observers.